## Linear Regression

Linear Regression. Fit the line y = mx + b to linear data where:
- x is the dependent variable
- y is the independent variable
- x
_{i} is the x value for i'th data point
- y
_{i} is the y value for the i'th data point
- N is the number of different standards are used
- y
_{ave} is the average of the y values for the standards
- x
_{ave} is the average of the x values for the standards.

This method assumes that there is no variance in the value for x and that each standard is analyzed once.

**Calculate Sums:**

**Calculate Slope and Intercept:**

**Uncertainty in Regression.** Assuming linear function and no replicates, the standard deviation about the regression is:

**Uncertainty in y**_{predicted}.

**Uncertainty in x**_{predicted}. For an unknown with an average signal y_{unk} from M replicates: